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Please give an example in $ \mathbb{R}^{n} $ of a set $ T $ that satisfies the upper bound of $ 14 $ in the Kuratowski Closure-Complement Theorem. Thanks!

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The standard example in $ \mathbb{R} $ is $$ (0,1) \cup (1,2) \cup \{ 3 \} \cup [(4,5) \cap \mathbb{Q}]. $$

You can refer to the Wikipedia article on the Kuratowski Closure-Complement Theorem.

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    $\begingroup$ However, the OP is asking for an example in $\mathbb{R}^{n}$. Is it trivial to construct such one from that in $\mathbb{R}$? $\endgroup$ – hengxin Jan 22 '14 at 5:11

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